Question

[Giang Nguyen]

cho đa thức E(x)=\(x^{2018}-2019x^{2017}+2019x^{2016}-2019x^{2015}+...+2019x^2-2019x+1\). Tính E(2018)

Answer 1

[O=C=O]

\(E\left(x\right)=x^{2018}-2019x^{2017}+2019x^{2016}-2019x^{2015}+...+2019x^2-2019x+1\)

Vì \(E\left(2018\right)\) nên :

\(\Rightarrow E\left(x\right)=2018^{2018}-2019.2018^{2017}+2019.2018^{2016}-2019.2018^{2015}+...+2019.2018^2-2019.2018+1\)

Tới đoạn này thì ghi dấu "=" rồi tính và làm tương tự

Answer 2

[Akai Haruma]

Lời giải

Ta có:

\(E(x)=x^{2018}-2019x^{2017}+2019x^{2016}-2019x^{2015}+...+2019x^2-2019x+1\)

\(E(x)=(x^{2018}-2018x^{2017})-(x^{2017}-2018x^{2016})+(x^{2016}-2018x^{2015})-....+(x^2-2018x)-x+1\)

\(E(x)=x^{2017}(x-2018)-x^{2016}(x-2018)+x^{2015}(x-8)-...+x(x-2018)-x+1\)

\(E(x)=(x-2018)(x^{2017}-x^{2016}+x^{2015}-...+x)-x+1\)

Suy ra \(E(2018)=-2018+1=-2017\)